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3rd Grade Math Worksheet - A Parent's Guide

Many educators, politicians, and parents believe the instruction of mathematics in the United States is in crisis mode, and
has been for some time. Indeed, recent test results show that American 15-year-olds were
outperformed by 29 other countries on math testing scores.
1 To help counter this crisis, educational, civic, and business leaders worked together
to develop the Common Core State Standards (CCSS).

The goal of Common Core is to establish consistent, nationwide guidelines of what children should be learning each school
year, from kindergarten all the way through high school, in English and math. Though CCSS
sets forth these criteria, states and school districts are tasked with developing curricula
to meet the standards.

The 2014-15 school year will be important for Common Core as the standards are fully implemented in many remaining states
of the 43 (and the District of Columbia) that have embraced their adoption. CCSS has its
advocates as well as its critics, and the debate on its merits has become more pronounced
in recent months. Irrespective of the political differences with Common Core, its concepts
are critical for students because the standards help with understanding the foundational
principles of how math works. This guide steers clear of most of the controversy surrounding
CCSS and primarily focuses upon the math your thirdgrader will encounter.

Common Core Standards

A stated objective of Common Core is to standardize academic guidelines nationwide. In other words, what third-graders are
learning in math in one state should be the same as what students of the same age are learning
in another state. The curricula may vary between these two states, but the general concepts behind
them are similar. This approach is intended to replace wildly differing guidelines among different
states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student
success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught
at every grade level, including third grade. However, CCSS actually calls for fewer topics at
each grade level. The Common Core approach (which is clearly influenced by so-called “Singapore
Math”—an educational initiative that promotes mastery instead of memorization) goes against many
state standards, which mandate a “mile-wide, inch-deep” curriculum in which children are being
taught so much in a relatively short span of time that they aren’t effectively becoming proficient
in the concepts they truly need to succeed at the next level. Hence, CCSS works to establish
an incredibly thorough foundation not only for the math concepts in future grades, but also toward
practical application for a lifetime.

For third grade, Common Core’s focus places a tremendous emphasis on introductory multiplication. Fractions also make their
first appearance, and two-dimensional shapes receive plenty of attention. Ultimately, this focus
will enable children to develop rigor in real-life situations by developing a base of conceptual
understanding and procedural fluency.

Critical Areas of Focus

Third grade is an absolutely essential year in terms of math education. Multiplication is a new concept to many students
this age, but is one that must be mastered—the sooner, the better—because so much subsequent
math, from fourth grade all the way through high school and beyond, will rely upon it. Of course,
more complex addition and subtraction, introductory fractions, and geometry aren’t ignored, but
multiplication (and, eventually, division) is the marquee attraction during this year. Here are
the four critical areas that Common Core brings to third-grade math:

Multiplication

Students will develop fluency multiplying single-digit numbers. Strategies used include repeated addition (e.g., 4x3 is the
same as 4+4+4), analyzing equal-sized groups, arrays, and area models, to arrive at a product.
Students also will eventually learn the relationship between multiplication and division (though
the really big Common Core push on division won’t occur until fourth grade).

Fractions

Fractions are another concept students will use for years to come. The idea of unit fractions (in
which the numerator is 1, such as in ½) is introduced first. Visual models will be used to demonstrate
that fractions are part of a whole. Adding and subtracting fractions won’t come until later grades,
but students will be taught to visually compare fractions (for example, four friends dividing
a pizza into four parts means each gets 1/4 of the pie; if they decided to divide into eight,
each would get two slices; from this students see that 1/4 is greater than 1/8).

Area

Tied into multiplication is the concept of area— especially in the sense that the space covered by
a square or rectangle is width times length. At first, students will compute area simply by counting
unit squares. Eventually, Tthe rectangular arrays used to help with multiplication come into
play (e.g., an array of 2 rows and 4 columns equals 8 units).

Shapes

Students will continue to identify and define two-dimensional shapes by sides and angles. Furthermore,
the fraction concepts introduced in third-grade will be tied into geometry—many of the visual
models used will involve circles, triangles, and rectangles divided into equal parts.

Overview of Topics

From the four critical areas of focus discussed in the previous section, Common Core also further clarifies the skills third-graders
should know by the end of the school year. For example, the fluency requirements at this level
are single-digit products and quotients (i.e., basic multiplication and division, with times
tables committed to memory by the end of the year) and adding and subtracting within 1,000. The
five topics presented here, taken directly from CCSS itself,
2 include some specifics on what kids will be taught in Grade 3.

Operations and Algebraic Thinking

Represent and solve problems using multiplication and division. Students will learn
to multiply single-digit numbers and divide numbers of less than 100 with whole quotients.
They will also apply these strategies to solving word problems

Understand the properties of multiplication and the relationship between multiplication and
division.
The concept that 7 × 3 is the same as 3 × 7 will be emphasized. Also, the complementary relationship between multiplication
and division will be introduced—for example, if 7 × 3=21, then 21 ÷ 3 =7 .

Multiply and divide numbers within 100. By the end of third grade, students will
be expected to know by memory all single-digit multiplication operations (i.e., times tables),
which in turn will provide fluency in division with these basic equations (in other words,
easy division without remainders).

Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Students will solve two-step word problems using the four basic operations (addition,
subtraction, multiplication, and division) as well as by estimation strategies such as rounding.
They will also identify and apply patterns within the math (for example, an odd number times
an odd number will always produce an odd number).

Number Operations in Base 10

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Students will strive toward fluently adding or subtracting numbers within a 1,000. They will master rounding numbers to the
nearest 10 or 100, and they will also learn to multiply one-digit numbers by multiples of
10 but less than 100 (e.g., 6 × 40).

Number Operations—Fractions

Develop understanding of fractions as numbers.
As third-graders get their first major exposure to fractions, many concepts will be introduced:

Students will understand the fraction 1/b as one part of a whole that is partitioned into b equal parts.

They will learn how to represent a fraction as part of a number line (between 0 and 1).

They will learn about equivalent fractions and be able to recognize simple equivalencies (e.g., 1/2 is the same a 2/4 and
5/10).

They will be able to compare fractions with the same numerator or denominator and determine which is larger or smaller.

Measurement and Data

Solve problems involving measurement and estimation. Students will learn to tell
time to the minute, as well as solve basic addition and subtraction word problems involving
time. Estimating The concept of volume and mass is introducedexplained, and third-graders
will be taught to solve one-step word problems with volumes or mass involving the same unit
(for example, one cup holds 8 ounces of juice and another holds 6 ounces; how much total
juice is there?).

Represent and interpret data.
Thirdgraders will draw scaled picture graphs to represent data (for example, a
graph in which one square equals three of an object), and they will solve one- or twostep
“how many more?” and “how many less?” word problems. Also, they will use rulers to gather
measurement data to within a quarter-inch and represent the results on a line plot.

Geometric measurement: Understand concepts of area and relate to multiplication and addition.
The idea of a “square unit” is introduced to better explain and work with area. Students will learn how to measure area by
counting the square units and by using addition and multiplying. The additive nature of area
will be introduced—students will be taught how to compute area of rectilinear shapes by breaking
them down into rectangles first.

Geometric measurement: Perimeter.
As a continuation of their understanding of area, Sstudents are introduced to the concept of perimeter. They will learn how
perimeter differs from area (for example, the perimeter of a fenced yard is how much fence
is needed, while the area is how much grass is growing within) and will will solve equations
and word problems involving the perimeter of polygons.

Geometry

Reason with shapes and their attributes.
Different categories of shapes (e.g., quadrilaterals) will be explained, and students will classify shapes according to sides,
angles, and so on. Coinciding with the introduction to fractions, thirdgraders will partition
shapes into parts with equal areas.

2Grade 4: Introduction, Common Core State Standards Initiative

The Truth About CCSS and Performance

Common Core aims to improve educational performance and standardize what students should learn at every grade in preparation
for a lifetime of application, but it does not set curricula, nor does it direct how teachers should
teach. As with any educational reform, some teachers, schools, and school districts will struggle
with CCSS, some will seamlessly adapt, and some will thrive. As a parent, your responsibility is
to monitor what your third-grader is learning, discover what is working or isn’t working for your
child, and to communicate with his or her teacher—and to accept that your children’s math instruction
does differ from what you learned when you were younger, or even what they might have learned last
year. The transition can be a little daunting for parent and student alike, but that’s not a product
of the standard itself. Common Core simply takes a new, more pointed approach to improving the quality
of math instruction in this country.

The Benefits

As previously mentioned, CCSS decreases the number of topics students learn at each grade. However, the remaining topics
are covered so extensively that the chances a child will master the corresponding skills increase.
An analogy to this approach is comparing two restaurants. One restaurant has a varied menu with dozens
of items; the other only serves hamburgers, fries, and milk shakes. The quality of the food at the
first restaurant may vary upon the cooks’ experience, the multitude of ingredients required for so
many offerings, and the efficiency (or lack thereof) of the staff. Because the second restaurant
only serves three items, mastering those three items efficiently should result in an excellent customer
experience. That’s not to say the first restaurant won’t succeed (because many do), but there’s always
a chance that something on the menu won’t live up to the business’s own expectations.

By reducing the number of math topics taught, Common Core helps ensure students are truly ready for what
comes next. Given the attention given to the included concepts, more practical applications and alternate
operations of the math can be explored.

Coinciding with the reduction of topics is an emphasis on vigor—achieving a “deep command” of the math being taught. Students
will be challenged to understand the concepts behind mathematical operations rather than just resorting
to rote memorization and processes to get a right answer. Speed and accuracy are still important;
kids won’t be getting away that easily from flash cards and quizzes that increase fluency. Moreover,
Common Core places even additional emphasis on practical application—after all, the math kids learn
now will be important when they become adults, even if they never have to think about prime numbers
or symmetrical lines in their day-to-day lives.

Finally, CCSS links standards from grade to grade so that the skills learned at one level translate into the tools they need
to learn at the next level. This coherence would seem an obvious educational approach, but often,
there is no link—students are taught a skill in third grade that might not be used (and might have
to be retaught) until fifth. Each new concept in Common Core is an extension of a previous, already
learned concept.

Math Practices to Help Improve Performance

In addition to the grade-specific standards it sets forth, Common Core also emphasizes eight “Standards of Mathematical Practice”
that teachers at all levels are encouraged to develop in their students.3 These eight practices,
designed to improve student performance, are described here, with added information on how they apply
to third-graders.

Make sense of problems and persevere in solving them
Students explain the problem to themselves and determine ways they can reach a solution. Then, they work at the problem until
it’s solved. For example, multiplication is brand new to third-graders, so word problems
involving the concept may be particularly challenging for students more conditioned to addition
and subtraction problems. This CCSS math practice encourages them to take their time to read
and try understanding the problem, emphasizing that the process is ultimately important even
if it doesn’t result in a correct answer. Third-graders will also be encouraged to use pictures
or objects to better visualize the problem and solution.

Reason abstractly and quantitatively
Students decontextualize and contextualize problems. By decontextualizing, they break down the problem into anything other
than the standard operation. By contextualizing, they apply math into problems that seemingly
have none. For example, if a third-grade word problem involves bananas in bunches of
10, students who are decontextualizing may represent each bunch by drawing one banana.
Kids this age who are contextualizing may organize bananas into bunches in a word problem
that doesn’t otherwise use such terminology.

Construct viable arguments and critique the reasoning of others
Students use their acquired math knowledge and previous results to explain or critique their work or the work of others.
With multiplication being so new, third-graders must become particularly adept at talking
about how they arrived at an answer with their newly acquired skills. Besides boosting
their confidence, the ability to explain the math will increase their ability to excel
at it.

Model with mathematics
This is just like it sounds: Students use math to solve real-world problems. Third-graders can be challenged to take the
math skills they have learned into their own lives. For example, student who eats three string
cheeses a day can use multiplication to figure out how many he eats during a week or a month.

Use appropriate tools strategically
Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. For third-graders,
the introduction of multiplication offers a pertinent example of this practice: The new concept
gives students another option when solving a problem. Take the equation 3 × 7—third-graders
can either add 7 + 7 + 7 to get the answer, or they can use their new skills to multiply
3 by 7 and arrive at the same result.

Attend to precision
Students strive to be exact and meticulous—period. The emphasis on committing times tables to memory demonstrates how precision
is so essential to multiplication; not knowing the answer to 4 × 6 now will lead to trouble
when trying to solve 14 × 36 in the future. Furthermore, if a student can’t come up with
the right answer on a more complex problem, he should be taking steps to figure out how or
should ask for help.

Look for and make use of structure
Students will look for patterns and structures within math and apply these discoveries to subsequent problems. For example,
third-graders might understand that multiplying even numbers together will produce an even
number, and then use that knowledge to help solve future equations.

Look for and express regularity in repeated reasoning
Students come to realizations—“aha” moments is a good term for these realizations—about the math operations that they are
performing and use this knowledge in subsequent problems. For example, a third-grader
may realize that 2 multiplied by any number is simply that number added to itself, and
then use addition strategies to get to the correct answer.

How to Help Your Children Succeed Beyond CCSS

Some of parents’ trepidation with Common Core isn’t so much with the guidelines themselves, but with the testing now aligned
with CCSS via local math curricula. Standardized testing was stressful for students and parents
before; with the ongoing Common Core implementation, many families simply don’t know what to
expect.

Fortunately, CCSS does not have to be that stressful, for you or your third-grader. Here are some tips to help your children
succeed with Common Core math:

Be informed; be involved

If Common Core concerns you, intrigues you, or confuses you, don’t hesitate to learn as much about it—in your child’s classroom,
at your kids’ school, and on a national level. Talk with teachers, principals, and other parents.
Seek advice on how you can help your kids, and yourself, navigate CCSS math. If you want to take
further action, become involved with PTA or other organizations and committees that deal with
your school’s curriculum. The more you know, the more, ultimately, you can help your child.

Give them some real-world math

A basic tenet of Common Core is to apply math principles to real-world situations. Why not start
now? Give your child math problems when you are out and about—the store, in traffic, the park,
and so on. For example, if you are at a basketball game and your child’s favorite player scores
6 points in the first quarter, ask her how many points the player might finish the game with
based on that initial statistic.

Take time to learn what they are learning

You might look at a worksheet your child brings home and think, “This isn’t the math I’m used to.”
Because Common Core emphasizes understanding the process of arriving at an answer, your child
may be taught additional ways to fry a mathematical egg, so to speak. Instead of shunning these
approaches, learn them for yourself. Once you comprehend these additional methods, you will be
better able to help your child comprehend them as well.

Encourage them to show their work

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer, especially
within Common Core. Second, ask your children to show you their homework, particularly the challenging
stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident
in explaining their work to you, they will carry that confidence into the classroom when the
teacher asks for those same explanations.

Seek more help if necessary

If your third-grader is struggling with the new math standards, talk with his or her teacher first. You then might want to
seek outside resources to help your child. Several online resources provide math help, including
worksheets and sample tests that conform to Common Core standards. Tutoring might be an option
you consider as well. Innovative iPadbased math programs have emerged that combine the personalized
approach of a tutor with today’s technology. This revolutionary approach also may feature a curriculum
based on Common Core, thus ensuring your child’s learning at home is aligned with what he or
she is learning at school.

Math Practice Worksheets

Operations and Algebraic Thinking

The store ordered 4 boxes of styli. There were 8 styli in each box. Which image shows
the total styli that the store ordered?

Ken gets 8 points and 3 stars for every Mario game he wins. If he wins 8 Mario games,
how many total points would he have?

Select the division statement for the array

18 ÷ 3 = 6

18 ÷ 2 = 9

18 ÷ 6 = 2

18 ÷ 3 = 8

Write the equivalent expression for the statement. How many sets of 5 are in 30?

30 ÷ 5

30 × 5

5 × 30

Find the missing number:

___ × 7 = 28

Find the missing numbers in the sequence.

9, 18, ___, 36, 45, ___

The table shows the relation between the meters of cloth used for stitching shirts. Which of the following describes the
pattern between the meters of cloth and the shirts?

Add 2

Multiply by 2

Multiply by 3

Add 3

Select the equivalent equation for the given statement. Amber got 16 gifts for Christmas.
Her brother got b fewer gifts than her. They got a total of 30 gifts.

16 + (16 − b) = 30

16 + (16 + b) = 30

16 − (16 + b) = 30

Computed value of 8 × 12 = _

Estimate the same by rounding off both the numbers to the nearest tens.

Estimated value of 8 × 12 = _ × _ = _

In a department store there are 83 glass bottles. 35 of those are damaged. The remaining
glass bottles are divided equally into 4 cartons. Find the number of glass bottles
in each carton.

Number Operations in Base 10

266 + 675 = __

160 − __ = 41

173 domestic flights and 163 international flights land at airport A. 145 domestic flights
and 133 international flights land at airport B. How many total international flights
land at these two airports?

Estimate the product by rounding the first factor to the nearest tens.

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